import math
def mystery(x):
"""
Find a value for x that makes this function return True.
x can be a string or a number.
"""
if not isinstance(x, float):
return False
# A seemingly random sequence of operations
try:
a = math.log(x)
b = math.tan(a)
c = math.sqrt(abs(b))
d = math.floor(c * 1000)
except (ValueError, TypeError):
# Catches things like log of a negative number
return False
# Check against a "magic" number
return d == 1337
import hashlib
import struct
def mystery(x):
"""
Find a value for x that makes this return True.
x can be a string or a number.
"""
# Normalize input to bytes in a slightly unfriendly way.
if isinstance(x, str):
b = x.encode("utf-8", "surrogatepass")
elif isinstance(x, (int, float)):
# Canonicalize numbers into an IEEE754 float64 byte pattern (big-endian)
try:
b = struct.pack(">d", float(x))
except Exception:
return False
else:
return False
# A small hash cascade (deterministic, but not obvious to invert by inspection).
h = hashlib.sha256(b).digest()
h = hashlib.blake2b(h, digest_size=32, person=b"mystery-v1").digest()
h = hashlib.sha1(h + b"\x00" + b[::-1]).digest() # 20 bytes
# Condition: first 3 bytes are all zero, and a parity check on the last 2 bytes.
if h[:3] != b"\x00\x00\x00":
return False
tail = h[-2:]
# Popcount parity of the last 16 bits must be even.
bits = int.from_bytes(tail, "big")
return (bits.bit_count() % 2) == 0
import uuid
def mystery(x):
"""
Find a value for x that makes this function return True.
x can be a string or a number.
"""
# The input must be interpretable as a UUID.
try:
# This handles strings like "65158531-332e-4b95-a423-356434304dc0"
# and will attempt to convert other types to string first.
u = uuid.UUID(str(x))
except (ValueError, TypeError, AttributeError):
return False
# The 128-bit integer representation of the UUID.
val = u.int
# The key is derived from the digits of Pi. It is a constant.
# It corresponds to the 101st to 132nd fractional digits of Pi,
# interpreted as a hexadecimal number.
pi_digits = "14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196"
key_hex = pi_digits[100:132] # 32 hex characters = 128 bits
key_val = int(key_hex, 16)
# The transformation is a 128-bit circular left shift by 3 bits.
mask = (1 << 128) - 1
transformed_val = ((val << 3) & mask) | (val >> (128 - 3))
# The condition to satisfy: a linear recurrence relation over GF(2).
return (val ^ transformed_val) == key_val
import math
import hashlib
import struct
def mystery(x):
"""
Find a value for x that makes this return True.
x can be a string or a number.
"""
# Normalize to bytes in a mildly awkward but deterministic way.
if isinstance(x, str):
b = x.encode("utf-8", "surrogatepass")
elif isinstance(x, int):
# Signed, minimal-length, big-endian (two's complement not used; sign stored separately)
if x == 0:
b = b"\x00"
else:
mag = abs(x)
blen = (mag.bit_length() + 7) // 8
b = mag.to_bytes(blen, "big")
if x < 0:
b = b"-" + b
elif isinstance(x, float):
# IEEE754 float64 big-endian
try:
b = struct.pack(">d", float(x))
except Exception:
return False
else:
return False
# A bunch of checks that look "crypto-ish".
# (Most inputs fail fast.)
h = hashlib.sha256(b + b"\x00" + b[::-1]).digest()
g = hashlib.blake2s(h, digest_size=16, key=b"mystery-key").digest()
# Seemingly tough constraints...
if (g[0] ^ g[5] ^ g[10] ^ g[15]) != 0xA7:
return False
if (sum(g) + len(b)) % 97 != 42:
return False
if (int.from_bytes(g[:4], "big") & 0x1FFFF) != 0x1C0DE:
return False
# ...but the real "needle" is hidden in a numeric identity that only triggers
# for a special float value.
if not isinstance(x, float):
return False
y = x - x # NaN stays NaN; ordinary numbers become 0.0 (including inf - inf => NaN)
# Only True when y is NaN.
return (y != y) and (math.isnan(y))
import zlib
import struct
def mystery(x):
"""
Find a value for x that makes this function return True.
x can be a string or a number.
"""
if not isinstance(x, str):
return False
try:
# The input is expected to be a hex-encoded string representing binary data.
data = bytes.fromhex(x)
except (ValueError, TypeError):
return False
# The data must conform to a specific binary structure.
# Header: 12 bytes
# - 4 bytes: Magic number (big-endian)
# - 4 bytes: CRC32 checksum (big-endian)
# - 4 bytes: Uncompressed payload size (big-endian)
# Body: N bytes
# - N bytes: zlib-compressed payload
if len(data) < 12:
return False
try:
# Unpack header as three big-endian unsigned integers
magic, crc_from_header, size_from_header = struct.unpack('>III', data[:12])
except struct.error:
return False
# 1. Check the magic number
if magic != 0xDECODEBEEF:
return False
compressed_payload = data[12:]
# 2. The CRC in the header must match the CRC of the *compressed* payload body.
# This is a crucial detail.
if zlib.crc32(compressed_payload) != crc_from_header:
return False
# 3. Decompress the payload
try:
payload = zlib.decompress(compressed_payload)
except zlib.error:
return False
# 4. The size in the header must match the actual decompressed size
if len(payload) != size_from_header:
return False
# 5. The decompressed payload must satisfy several mathematical conditions
# Condition A: It must be a byte-wise palindrome
if payload != payload[::-1]:
return False
# Condition B: Its length must be a prime number
p_len = len(payload)
is_prime = p_len > 1 and all(p_len % i != 0 for i in range(2, int(p_len**0.5) + 1))
if not is_prime:
return False
# Condition C: When interpreted as a big-endian integer, it must be divisible by 1337
if int.from_bytes(payload, 'big') % 1337 != 0:
return False
return True
import math
import struct
import hashlib
def mystery(x):
"""
Find a value for x that makes this function return True.
x can be a string or a number.
"""
# Normalize to bytes in a deliberately fiddly way.
if isinstance(x, str):
try:
b = x.encode("utf-8", "surrogatepass")
except Exception:
return False
elif isinstance(x, int):
# Signed magnitude encoding with a length prefix
sign = b"\x01" if x < 0 else b"\x00"
mag = abs(x)
blen = max(1, (mag.bit_length() + 7) // 8)
b = sign + bytes([blen]) + mag.to_bytes(blen, "big")
elif isinstance(x, float):
# Canonical float bytes
try:
b = b"F" + struct.pack(">d", float(x))
except Exception:
return False
else:
return False
# Distracting "crypto-ish" filter that looks like it makes inversion hard.
h = hashlib.blake2s(b, digest_size=16, key=b"mystery-key").digest()
# A couple of opaque constraints
if (h[0] ^ h[7] ^ h[15]) != 0x5C:
return False
if (sum(h) + len(b)) % 251 != 137:
return False
# Now the real gate: a floating-point corner case.
# Only a NaN satisfies (x != x).
if not isinstance(x, float):
return False
return (x != x) and math.isnan(x)
import hashlib
def mystery(x):
"""
Find a value for x that makes this function return True.
x can be a string or a number.
"""
if not isinstance(x, str) or not all(c in 'UDLR' for c in x):
return False
GRID_SIZE = 64
START_POS = (0, 0)
TARGET_POS = (GRID_SIZE - 1, GRID_SIZE - 1)
# These seeds deterministically generate the maze layout.
SEED_WALLS = "The only winning move is not to play."
SEED_PORTALS = "How about a nice game of chess?"
# A memoized helper function to determine if a cell is a wall.
# The cache is reset for each call to mystery.
_wall_cache = {}
def is_wall(r, c):
if (r, c) in _wall_cache:
return _wall_cache[(r, c)]
# The wall layout is pseudo-random, based on a hash of the coordinates.
h = hashlib.sha256(f"{r}:{c}:{SEED_WALLS}".encode()).digest()
# Approx. 20% of cells are walls (51/256).
result = h[0] < 51
_wall_cache[(r, c)] = result
return result
# Initial position
pos_r, pos_c = START_POS
# The maze is defined implicitly. We simulate the path given by x.
for move in x:
next_r, next_c = pos_r, pos_c
if move == 'U':
next_r -= 1
elif move == 'D':
next_r += 1
elif move == 'L':
next_c -= 1
elif move == 'R':
next_c += 1
# Check for invalid moves (out of bounds or into a wall).
# Such moves are simply ignored; the turn is wasted.
if not (0 <= next_r < GRID_SIZE and 0 <= next_c < GRID_SIZE):
continue
if is_wall(next_r, next_c):
continue
# Valid move, update position.
pos_r, pos_c = next_r, next_c
# Check if the new cell is a portal.
h = hashlib.sha256(f"{pos_r}:{pos_c}:{SEED_PORTALS}".encode()).digest()
# Approx. 5% of cells are portals (13/256).
is_portal = h[0] < 13
if is_portal:
# The portal destination is also derived from the hash.
dest_r, dest_c = (h[1] % GRID_SIZE, h[2] % GRID_SIZE)
# A portal leading into a wall is a dud; it does nothing.
if not is_wall(dest_r, dest_c):
pos_r, pos_c = dest_r, dest_c
return (pos_r, pos_c) == TARGET_POS
import hashlib
import struct
def mystery(x):
"""
Find a value for x that makes this function return True.
x can be a string or a number.
"""
# Normalize x into bytes in a slightly unfriendly way.
if isinstance(x, str):
b = x.encode("utf-8", "surrogatepass")
tag = b"S"
elif isinstance(x, int):
# Signed two's-complement, minimal length, big-endian
if x == 0:
b = b"\x00"
else:
nbits = x.bit_length() + 1 # include sign
nbytes = (nbits + 7) // 8
b = int(x).to_bytes(nbytes, "big", signed=True)
tag = b"I"
elif isinstance(x, float):
# Canonical IEEE-754 float64 big-endian
try:
b = struct.pack(">d", float(x))
except Exception:
return False
tag = b"F"
else:
return False
# "Looks crypto": cascade and bit-tests
h1 = hashlib.sha256(tag + b + b"\x00" + b[::-1]).digest()
h2 = hashlib.blake2s(h1, digest_size=16, person=b"mystery/v2").digest()
# Opaque constraints that appear to require search
if (h2[0] ^ h2[5] ^ h2[10] ^ h2[15]) != 0x00:
return False
if (int.from_bytes(h2[:4], "big") & 0x1FFF) != 0x1A2B:
return False
if (sum(h2) % 251) != 0:
return False
# Final twist: there is exactly one easy way through.
# For IEEE-754 NaN, comparisons are always False except != is True.
if not isinstance(x, float):
return False
return (x != x)
import cmath
import hashlib
def mystery(x):
"""
Find a value for x that makes this function return True.
x can be a string or a number.
"""
if not isinstance(x, (int, float, complex)):
return False
# The puzzle is to find a root of a specific polynomial.
# The coefficients are derived from a hash to make them non-obvious.
seed = b"the root of all evil is the lack of money"
h = hashlib.sha256(seed).digest()
# We construct a degree-7 polynomial P(z) = c[0]*z^7 + c[1]*z^6 + ... + c[7]
# The coefficients are derived from the hash bytes.
coeffs = []
for i in range(8):
# Each coefficient is a complex number.
# Its real and imaginary parts are built from 2 bytes each.
# Dividing by 1000.0 scales them to a reasonable range.
real = int.from_bytes(h[i*4 : i*4+2], 'big', signed=True) / 1000.0
imag = int.from_bytes(h[i*4+2 : i*4+4], 'big', signed=True) / 1000.0
coeffs.append(complex(real, imag))
# Evaluate the polynomial P(x) using Horner's method.
# This is equivalent to:
# val = coeffs[0]*x**7 + coeffs[1]*x**6 + ... + coeffs[7]
# but more numerically stable and efficient.
val = complex(0, 0)
for c in coeffs:
val = val * x + c
# A number 'x' is a root if P(x) is very close to zero.
# We must allow for floating point inaccuracies.
return abs(val) < 1e-9
import hashlib
import struct
def mystery(x):
"""
Find an x (string or number) such that this returns True.
"""
# Normalize x -> bytes
if isinstance(x, str):
b = x.encode("utf-8", "surrogatepass")
tag = b"S"
elif isinstance(x, int):
# minimal signed big-endian
if x == 0:
b = b"\x00"
else:
nbytes = max(1, (x.bit_length() + 8) // 8)
b = int(x).to_bytes(nbytes, "big", signed=True)
tag = b"I"
elif isinstance(x, float):
b = struct.pack(">d", float(x))
tag = b"F"
else:
return False
# A "crypto-ish" cascade to look nasty
h = hashlib.blake2s(tag + b, digest_size=16, key=b"mystery-key").digest()
g = hashlib.sha256(h + b[::-1]).digest()
# Constraints that appear to force searching
if (g[0] ^ g[11] ^ g[22] ^ g[31]) != 0xA6:
return False
if (sum(g) + len(b)) % 251 != 117:
return False
if (int.from_bytes(g[12:16], "big") & 0x00FF00FF) != 0x002A00C0:
return False
# The actual "needle": one specific IEEE-754 payload.
# Must be a quiet NaN with payload ending ...C0DE.
if not isinstance(x, float):
return False
u = int.from_bytes(struct.pack(">d", float(x)), "big")
exp = (u >> 52) & 0x7FF
frac = u & ((1 << 52) - 1)
# NaN check + payload check
return (exp == 0x7FF) and (frac != 0) and ((u & 0xFFFF) == 0xC0DE)